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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.random;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    /**<a name="line.24"></a>
<FONT color="green">025</FONT>     * &lt;p&gt;This class provides a stable normalized random generator. It samples from a stable<a name="line.25"></a>
<FONT color="green">026</FONT>     * distribution with location parameter 0 and scale 1.&lt;/p&gt;<a name="line.26"></a>
<FONT color="green">027</FONT>     *<a name="line.27"></a>
<FONT color="green">028</FONT>     * &lt;p&gt;The implementation uses the Chambers-Mallows-Stuck method as described in<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;i&gt;Handbook of computational statistics: concepts and methods&lt;/i&gt; by<a name="line.29"></a>
<FONT color="green">030</FONT>     * James E. Gentle, Wolfgang H&amp;auml;rdle, Yuichi Mori.&lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     *<a name="line.31"></a>
<FONT color="green">032</FONT>     * @version $Id: StableRandomGenerator.java 1394763 2012-10-05 19:54:00Z psteitz $<a name="line.32"></a>
<FONT color="green">033</FONT>     * @since 3.0<a name="line.33"></a>
<FONT color="green">034</FONT>     */<a name="line.34"></a>
<FONT color="green">035</FONT>    public class StableRandomGenerator implements NormalizedRandomGenerator {<a name="line.35"></a>
<FONT color="green">036</FONT>        /** Underlying generator. */<a name="line.36"></a>
<FONT color="green">037</FONT>        private final RandomGenerator generator;<a name="line.37"></a>
<FONT color="green">038</FONT>    <a name="line.38"></a>
<FONT color="green">039</FONT>        /** stability parameter */<a name="line.39"></a>
<FONT color="green">040</FONT>        private final double alpha;<a name="line.40"></a>
<FONT color="green">041</FONT>    <a name="line.41"></a>
<FONT color="green">042</FONT>        /** skewness parameter */<a name="line.42"></a>
<FONT color="green">043</FONT>        private final double beta;<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>        /** cache of expression value used in generation */<a name="line.45"></a>
<FONT color="green">046</FONT>        private final double zeta;<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /**<a name="line.48"></a>
<FONT color="green">049</FONT>         * Create a new generator.<a name="line.49"></a>
<FONT color="green">050</FONT>         *<a name="line.50"></a>
<FONT color="green">051</FONT>         * @param generator underlying random generator to use<a name="line.51"></a>
<FONT color="green">052</FONT>         * @param alpha Stability parameter. Must be in range (0, 2]<a name="line.52"></a>
<FONT color="green">053</FONT>         * @param beta Skewness parameter. Must be in range [-1, 1]<a name="line.53"></a>
<FONT color="green">054</FONT>         * @throws NullArgumentException if generator is null<a name="line.54"></a>
<FONT color="green">055</FONT>         * @throws OutOfRangeException if {@code alpha &lt;= 0} or {@code alpha &gt; 2}<a name="line.55"></a>
<FONT color="green">056</FONT>         * or {@code beta &lt; -1} or {@code beta &gt; 1}<a name="line.56"></a>
<FONT color="green">057</FONT>         */<a name="line.57"></a>
<FONT color="green">058</FONT>        public StableRandomGenerator(final RandomGenerator generator,<a name="line.58"></a>
<FONT color="green">059</FONT>                                     final double alpha, final double beta)<a name="line.59"></a>
<FONT color="green">060</FONT>            throws NullArgumentException, OutOfRangeException {<a name="line.60"></a>
<FONT color="green">061</FONT>            if (generator == null) {<a name="line.61"></a>
<FONT color="green">062</FONT>                throw new NullArgumentException();<a name="line.62"></a>
<FONT color="green">063</FONT>            }<a name="line.63"></a>
<FONT color="green">064</FONT>    <a name="line.64"></a>
<FONT color="green">065</FONT>            if (!(alpha &gt; 0d &amp;&amp; alpha &lt;= 2d)) {<a name="line.65"></a>
<FONT color="green">066</FONT>                throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_LEFT,<a name="line.66"></a>
<FONT color="green">067</FONT>                        alpha, 0, 2);<a name="line.67"></a>
<FONT color="green">068</FONT>            }<a name="line.68"></a>
<FONT color="green">069</FONT>    <a name="line.69"></a>
<FONT color="green">070</FONT>            if (!(beta &gt;= -1d &amp;&amp; beta &lt;= 1d)) {<a name="line.70"></a>
<FONT color="green">071</FONT>                throw new OutOfRangeException(LocalizedFormats.OUT_OF_RANGE_SIMPLE,<a name="line.71"></a>
<FONT color="green">072</FONT>                        beta, -1, 1);<a name="line.72"></a>
<FONT color="green">073</FONT>            }<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>            this.generator = generator;<a name="line.75"></a>
<FONT color="green">076</FONT>            this.alpha = alpha;<a name="line.76"></a>
<FONT color="green">077</FONT>            this.beta = beta;<a name="line.77"></a>
<FONT color="green">078</FONT>            if (alpha &lt; 2d &amp;&amp; beta != 0d) {<a name="line.78"></a>
<FONT color="green">079</FONT>                zeta = beta * FastMath.tan(FastMath.PI * alpha / 2);<a name="line.79"></a>
<FONT color="green">080</FONT>            } else {<a name="line.80"></a>
<FONT color="green">081</FONT>                zeta = 0d;<a name="line.81"></a>
<FONT color="green">082</FONT>            }<a name="line.82"></a>
<FONT color="green">083</FONT>        }<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>        /**<a name="line.85"></a>
<FONT color="green">086</FONT>         * Generate a random scalar with zero location and unit scale.<a name="line.86"></a>
<FONT color="green">087</FONT>         *<a name="line.87"></a>
<FONT color="green">088</FONT>         * @return a random scalar with zero location and unit scale<a name="line.88"></a>
<FONT color="green">089</FONT>         */<a name="line.89"></a>
<FONT color="green">090</FONT>        public double nextNormalizedDouble() {<a name="line.90"></a>
<FONT color="green">091</FONT>            // we need 2 uniform random numbers to calculate omega and phi<a name="line.91"></a>
<FONT color="green">092</FONT>            double omega = -FastMath.log(generator.nextDouble());<a name="line.92"></a>
<FONT color="green">093</FONT>            double phi = FastMath.PI * (generator.nextDouble() - 0.5);<a name="line.93"></a>
<FONT color="green">094</FONT>    <a name="line.94"></a>
<FONT color="green">095</FONT>            // Normal distribution case (Box-Muller algorithm)<a name="line.95"></a>
<FONT color="green">096</FONT>            if (alpha == 2d) {<a name="line.96"></a>
<FONT color="green">097</FONT>                return FastMath.sqrt(2d * omega) * FastMath.sin(phi);<a name="line.97"></a>
<FONT color="green">098</FONT>            }<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>            double x;<a name="line.100"></a>
<FONT color="green">101</FONT>            // when beta = 0, zeta is zero as well<a name="line.101"></a>
<FONT color="green">102</FONT>            // Thus we can exclude it from the formula<a name="line.102"></a>
<FONT color="green">103</FONT>            if (beta == 0d) {<a name="line.103"></a>
<FONT color="green">104</FONT>                // Cauchy distribution case<a name="line.104"></a>
<FONT color="green">105</FONT>                if (alpha == 1d) {<a name="line.105"></a>
<FONT color="green">106</FONT>                    x = FastMath.tan(phi);<a name="line.106"></a>
<FONT color="green">107</FONT>                } else {<a name="line.107"></a>
<FONT color="green">108</FONT>                    x = FastMath.pow(omega * FastMath.cos((1 - alpha) * phi),<a name="line.108"></a>
<FONT color="green">109</FONT>                        1d / alpha - 1d) *<a name="line.109"></a>
<FONT color="green">110</FONT>                        FastMath.sin(alpha * phi) /<a name="line.110"></a>
<FONT color="green">111</FONT>                        FastMath.pow(FastMath.cos(phi), 1d / alpha);<a name="line.111"></a>
<FONT color="green">112</FONT>                }<a name="line.112"></a>
<FONT color="green">113</FONT>            } else {<a name="line.113"></a>
<FONT color="green">114</FONT>                // Generic stable distribution<a name="line.114"></a>
<FONT color="green">115</FONT>                double cosPhi = FastMath.cos(phi);<a name="line.115"></a>
<FONT color="green">116</FONT>                // to avoid rounding errors around alpha = 1<a name="line.116"></a>
<FONT color="green">117</FONT>                if (FastMath.abs(alpha - 1d) &gt; 1e-8) {<a name="line.117"></a>
<FONT color="green">118</FONT>                    double alphaPhi = alpha * phi;<a name="line.118"></a>
<FONT color="green">119</FONT>                    double invAlphaPhi = phi - alphaPhi;<a name="line.119"></a>
<FONT color="green">120</FONT>                    x = (FastMath.sin(alphaPhi) + zeta * FastMath.cos(alphaPhi)) / cosPhi *<a name="line.120"></a>
<FONT color="green">121</FONT>                        (FastMath.cos(invAlphaPhi) + zeta * FastMath.sin(invAlphaPhi)) /<a name="line.121"></a>
<FONT color="green">122</FONT>                         FastMath.pow(omega * cosPhi, (1 - alpha) / alpha);<a name="line.122"></a>
<FONT color="green">123</FONT>                } else {<a name="line.123"></a>
<FONT color="green">124</FONT>                    double betaPhi = FastMath.PI / 2 + beta * phi;<a name="line.124"></a>
<FONT color="green">125</FONT>                    x = 2d / FastMath.PI * (betaPhi * FastMath.tan(phi) - beta *<a name="line.125"></a>
<FONT color="green">126</FONT>                        FastMath.log(FastMath.PI / 2d * omega * cosPhi / betaPhi));<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>                    if (alpha != 1d) {<a name="line.128"></a>
<FONT color="green">129</FONT>                        x = x + beta * FastMath.tan(FastMath.PI * alpha / 2);<a name="line.129"></a>
<FONT color="green">130</FONT>                    }<a name="line.130"></a>
<FONT color="green">131</FONT>                }<a name="line.131"></a>
<FONT color="green">132</FONT>            }<a name="line.132"></a>
<FONT color="green">133</FONT>            return x;<a name="line.133"></a>
<FONT color="green">134</FONT>        }<a name="line.134"></a>
<FONT color="green">135</FONT>    }<a name="line.135"></a>




























































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